Question

(x+1/x)=15,x^2+1/x^2=?​

Answer 1

Answer:

Given, (x-1)/x = 15/4

        ⇒4(x-1) = 15x

        ⇒4x - 4 = 15x

        ⇒4x - 15x = 4

        ⇒-11x = 4

        ⇒ x = -4/11             ....eqn. 1

Now,

      (x-1)/x = 15/4

    Squaring both sides,

     ⇒{(x-1)/x}^2 = (15/4)^2

     ⇒(x^2 + 1 -2x)/x^2 = 225/16

   On adding 4x/(x^2) both sides and solving, you will get

    (x^2 + 1 + 2x)/(x^2) = 225/16 + 4x/(x^2)

   Now, SUBSTITUTE THE VALUE OF x WE GOT, IN RHS ONLY from eqn. 1.  

    And Solve... You will get

    ⇒(x^2 + 1 + 2x)/(x^2) = 49/16

    ⇒{(x+1)/x}^2 = (7/4)^2

    ∴ (x + 1)/x = 7/4 (Ans.)

Answer 2

Answer:

x²+1/x²=223

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